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Course unit, curriculum year 2020–2021
MATH.MA.830
Advanced Functional Analysis, 5 cr
Tampere University
- Description
- Completion options
Teaching periods
Course code
MATH.MA.830Language of instruction
EnglishAcademic year
2020–2021Level of study
Advanced studiesGrading scale
General scale, 0-5Persons responsible
Responsible teacher:
Lassi PaunonenResponsible organisation
Faculty of Information Technology and Communication Sciences 100 %
Core content
- Closed operators on Banach spaces, definition and characterizations
- Baire Category Theorem, Closed-Graph Theorem, Open Mapping Theorem, Uniform Boundedness Principle
- Operator representation of partial differential equations and the fundamental nature of differential operators
- Theory of Sobolev spaces, definitions and fundamental meaning
- Fredholm theory and regularity for PDEs, fundamental concepts
Complementary knowledge
- Basic techniques, verifying closedness in example cases
- Understanding the outlines of the proofs and the main applications of the results
- Ability to cast simple PDE examples in the operator theoretic framework
- Identifying the role of Sobolev spaces in the analysis of PDEs
- Understanding of the main role of Fredholm theory in the analysis of PDEs
Specialist knowledge
- Identifying and utilizing closedness of an operator as a tool for analysis
- Understanding the technical deails of the proofs and identifying the utilized proof techniques
- Ability to cast complicated PDE examples in the operator theoretic framework
- Ability to independently utilize Sobolev spaces in the analysis of PDEs
- Analysis of spectrum and regularity of solutions of PDEs
Learning outcomes
Prerequisites
Compulsory prerequisites
Further information
Learning material
Equivalences
Studies that include this course
Completion option 1
Completion of all options is required.
Exam
No scheduled teaching
Participation in teaching
No scheduled teaching